Description

In physics one often deals with systems comprised of composite particles that arise from the interaction of
fundamental constituents. Examples include atoms and complex molecules, the atomic core or hadrons in
general. When a large scale separation exists between the binding energy of such states and other system
scales (e.g. energy or matter density, temperature or pressure), these composite particles can be regarded as
essentially fundamental themselves, which enables the description in terms of effective models. The situation
becomes challenging, however, when such clear scale separation is absent. To systematically develop theories
that can tackle this universal challenge, experimental systems are required that allow one to make universal
connections between different fields of research to controllably benchmark theoretical approaches. Singlewalled
Carbon nanotubes (CNT) offer such a unique experimental platform. This semiconducting class of
materials is of direct technological relevance due to its unique opto-electronic properties. Importantly, in CNT
charge carriers (electrons and holes) can form composite, charge-neutral excitonic states which, in turn, can
bind additional electrons to form charged trion complexes. Both excitons and trions have been observed and,
due to the increased role of interactions in such quasi-one dimensional materials, are so deeply bound that
they remain robust quasiparticles even at room temperature. Recent experimental advances now allow chargecarrier
doping such that the system can be tuned to the regime where the scale separation between binding
energies of exciton and trions (analogs of hadrons in the context of QCD) and charge carrier densities looses
its validity.

In this project we will make use of this current experimental progress and the theoretical expertise built within
ISOQUANT to systematically develop a first unified effective theory for the many-body physics of electrons, excitons,
and trions in CNT and study the transition of this technolgically relevant many-body system from being
described by an effective theory of composite quasiparticles to a system governed by the dynamics of fundamental
charge carriers. Specifically we will derive an effective theory for exciton-electron scattering in CNT
and predict the optical response of CNT as a function of the doping. Using a hybrid wave function—functional
renormalisation group approach we will develop an effective theory that can describe the transition from the
low- and high-doping regime that can be benchmarked against methods developed in project C01. Based on
this theory we will explore perspectives for realising novel correlated electron states in CNT and we will study
means to employ exciton-electron interactions to realise sensing of such a correlated state with optical probes.